Return to Flatland

Whoever first referred to Economics as ‘The Dismal Science’ had clearly never read an article on ‘3Dness’ in drug discovery.  My own experience reading articles on this topic is a sensation of having my life force slowly sucked out (I even suggested that reviewing the '3Dness' literature might be considered as an appropriate penance when I recently confessed my sins at St Gallen Cathedral) and the subject of Confession reminds me of a song that the late great Tom Lehrer sang about the Second Vatican Council.

In this post I review the CNM2025 study (Return to Flatland) which examines the heavily-cited LBH2009 study (Escape from Flatland: Increasing Saturation as an Approach to Improving Clinical Success).This also is a good point to mention a Journal of Medicinal Chemistry Editorial (Property-Based Drug Design Merits a Nobel Prize) that I reviewed in a 30-Jul-2024 post. The CNM2025 study, which has already been reviewed by Dan and Ash, opens with: 

The year is 2009, Barack Obama has just been inaugurated and both Lady Gaga and The Black Eyed Peas are at the height of their popularity

This couldn’t help but remind me of the “WORLD WAR 2 BOMBER FOUND ON MOON” headline that appeared on the front page of the Sunday Sport twenty-one years before the publication of LBH2009 (it was was accompanied by a photo of a B-17 in a lunar crater). A few weeks later the headline was “WORLD WAR 2 BOMBER FOUND ON MOON VANISHES” (this time accompanied by a photo of the now empty lunar crater).

I’ll start my review of CNM2025 by quoting from it and, as is usual for posts here at Molecular Design, quoted text is indented with any comments by me italicized in red and enclosed in square brackets. 

The hypothesis was attractive, and the data clearly showed the relationship between Fsp³ and clinical progression with pairwise significance P < 0.001. [This statement is inaccurate and Figure 3 of the LBH2009 study shows statistically significant differences at this level between (a) discovery and phase 2 compounds (b) phase 1 and phase 3 compounds (c) phase 2 compounds & drugs.  The authors of LBH2009 state: “The change in average Fsp³ was statistically significant between adjacent stages in only one case (phase 1 to phase 2)” but they neither show this in Figure 3 of their article nor do they report a P-value for the statistical significance of the mean difference in Fsp³ between phase 1 and phase 2 compounds.] The statistics seemed compelling, though the effect size was modest — an increase in average Fsp³ of 0.09 between sets of phase I and approved drugs equates to a difference of around two additional sp³ carbons per drug molecule only. [The authors of LBH2009 did not actually report this difference to be statistically significant so it is unclear why the authors of CNM2025 have stated that the “statistics seemed compelling”.]

The LBH2009 study is effectively a call to think beyond aromatic rings in drug design and my view is that there are considerable benefits in doing so even though I consider the data analysis in the study to be shaky. Almost three decades ago I included a quinuclidine in the Zeneca fragment library for NMR screening and later at AstraZeneca I would actively search (with minimal success) for amides and heteroaryls derived from bicyclic amines. I see the advantages in looking beyond aromatic rings as stemming primarily from increased molecular diversity and a more controllable coverage of chemical space, and in KM2013 we wrote:

Molecular recognition considerations suggest a focus on achieving axial substitution in saturated rings with minimal steric footprint, for example by exploiting the anomeric effect or by substituting N-acylated cyclic amines at C2.

Although data analyses (for example, see HY2010) presented in support of the belief that aromatic rings adversely affect aqueous solubility are typically underwhelming I consider the suggestion to be plausible and suggested in K2022 that deleterious effects of aromatic rings are more likely to be due to their potential for making molecular interactions than to their planarity. That said, I should also point out that the analysis of the relationship between aqueous solubility and Fsp³ presented in Figure 5 of LBH2009 is a textbook example of correlation inflation (see Fig. 5 in KM2013) and I suspect that if a team had submitted this analysis at Statistiques Sans Frontières the judges would have either awarded “nul points” or come to the conclusion that the team had played its joker. Given the Lady Gaga reference in CNM2025 I couldn't resist linking this Peter Gabriel song which includes the lyrics "Adolf builds a bonfire, Enrico plays with it" even though I have absolutely no idea what the the lyrics actually mean.

While the analysis of the relationship between aqueous solubility presented in Figure 5 of LBH2009 does endow the study with what I’ll politely call a whiff of the pasture it’s not directly related to the analysis of clinical progression presented in the study. Let’s take a look at Figure 3 in LBH2009 which shows mean Fsp³ values for compounds in discovery, at the three phases of clinical development, and approved drugs. As an aside this analysis would fall foul of current Journal of Medicinal Chemistry author guidelines (see link; accessed 05-Aug-2025) which clearly mandate that “If average values are reported from computational analysis, their variance must be documented”.  As mentioned earlier in this post Figure 3 in LBH2009 shows statistically significant (P value < 0.001) differences between (a) discovery and phase 2 compounds (b) phase 1 and phase 3 compounds (c) phase 2 compounds & drugs. It’s also worth stressing that Figure 3 in LBH2009 does not show statistically significant differences in Fsp³ for any of the clinical development transitions (phase 1 to phase 2; phase 2 to phase 3; phase 3 to approved drug). Figure 3 of in LBH2009 shows 591 phase 2 compounds but only 376 phase 1 compounds, raising questions about the numbers of compounds that have been in clinical development without being recorded in the database.

I think that there are some problems with how the authors of the LBH2009 study have analysed the relationship between Fsp³ and progression through the stages of clinical development.  If charged with analysing this data I would focus on the three clinical development transitions (phase 1 to phase 2; phase 2 to phase 3; phase 3 to approved drug) and wouldn’t waste time on comparisons between discovery compounds and clinical compounds. If analysing the relationship between Fsp³ and the progression from phase 1 to phase 2, I would partition the set of phase 1 compounds into a ‘YES’ subset of compounds that had progressed to phase 2 and a ‘NO’ subset of compounds that had not progressed to phase 2. I would certainly be taking a close  look at distributions of Fsp³ values (some approaches to assessing statistical significance are based on the assumption of Normally-distributed data values) and I’d also be thinking about assessing effect size in addition to statistical significance. However, the problems with the LBH2009 analysis are more fundamental than non-Normal distributions of Fsp³ values.

The authors of LBH2009 assess the progression from phase 1 to phase 2 by comparing the mean Fsp³ value for the phase 1 compounds with the mean Fsp³ value for phase 2 compounds. The problem is that the Fsp³ values for the YES compounds (that have progressed from phase 1 to phase 2) are present in both the data sets for which comparisons are being made. This means that the observed differences in mean Fsp³ values will reflect both the difference between YES and NO compounds (relevant to relationship between Fsp³ and progression from phase 1 to phase 2) and the relative numbers of YES and NO compounds in the phase 1 data (not relevant to relationship between Fsp³ and progression from phase 1 to phase 2). Analysing the data in the way that the authors of LBH2009 have done effectively adds noise to the signal and it’s possible that they would have observed more statistically significant differences in mean Fsp³ values had they analysed the data in a more appropriate manner.

This is an appropriate point at which to discuss correlation in the context of studies such as LBH2009 and CNM2025. It’s actually well known (see L2013) that that Fsp³ values for chemical structures tend to be greater when amine nitrogen atoms are present (this does not invalidate the observed trends in the data but has big implications for how you interpret these trends). There is, however, a much bigger issue which is that correlation does not imply causation. Let’s suppose that you’ve just joined a drug discovery team as they are preparing to select a clinical candidate (I concede that this is most improbable scenario but it does illustrate a point). The team have an excellent understanding of the structure-activity relationship (SAR) and have successfully addressed a number of issues during the lead optimization process (the chemical structures of the compounds have been quite literally shaped by the problems that the team members have solved). Now consider the likely reaction of the team members to a suggestion that probability of success in the clinic would increase if the chemical structure of the best compound were modified so as to increase its Fsp³ value. My view is that the team might think that the person making such a suggestion had just stepped off the shuttle from Planet Tharg (an alien from this planet used to make occasional Sunday Sport  appearances). I see the trends in data observed by the authors of LBH2009 as effects rather than causes (the vanishing B-17 was never there in the first place).

Let’s return to the CNM2025 study and its authors state:

Using data from the Cortellis Drug Discovery Intelligence database, we repeated an analysis similar to that of Lovering et al. to assess Fsp³ in drugs approved post-2009 and those in active clinical development as of mid-2024 (Fig. 1). [I would challenge the claim that the analysis presented in CNM2025 is similar to that presented in LBH2009. The supplementary material for CNM2025 indicates that the data summarised in Fig. 1b correspond to the period 2012 through 2024 (it is not clear whether the database has been updated to account for compounds that have fallen out of active development during this period. As is the case for Figure 3 in LBH2009, Fig.1b in CNM2025 shows more phase 2 compounds (816) than phase 1 compounds (421), raising similar questions about the numbers of compounds that have been in clinical development without being recorded in the database. I thank fellow blogger  Dan Erlanson for suggesting that I examine the supplemental information for CNM2025.] Although our methods used contemporary data sources different to Lovering et al., we obtained comparable Fsp³ data for approved drugs prior to 2009. More recently however, the picture appears to have changed with approvals shifting to lower Fsp³ drugs (Fig. 1a). Similarly, when looking at drugs currently in clinical development (Fig. 1b), there appeared to be no clear relationship between highest phase reached and Fsp³, suggesting the key conclusion noted by Lovering et al. has not persisted. In all data sets, exemplars with Fsp³ = 0 as well as Fsp³ = 1 are extensively seen. [It is necessary to account for the number of hypotheses have been tested for statistical significance when quoting P-values (see R2016 and VM2018).]

Fig. 1a in CNM2025 shows the time-dependence of Fsp³ distributions for approved drugs according to approval date and I remain unconvinced of the value of analysis like this (on first encountering analysis of time-dependence of drug properties a quarter of a century ago I recall being left with the distinct impression that some senior medicinal chemists where I worked had a bit too much time on their hands). However, it is immaterial whether or not you are as underwhelmed as I am by time-dependence of drug properties because no such analysis is actually reported in LBH2009 and this is one reason that I challenge the claim by made by the authors of CNM2025 that they “repeated an analysis similar to that of Lovering et al. to assess Fsp³ in drugs approved post-2009 and those in active clinical development as of mid-2024”.  

Now let’s take a look at Fig. 1b in CNM2025 and this should be compared with Figure 3 in LBH2009. In some ways the former is an improvement on the latter since the violin plots show the distributions of Fsp³ values for each group of compounds and, as mentioned earlier in the post, I don’t think that it makes any sense to include discovery compounds in analysis like this (as the authors of LBH2009 did). Although these two figures look superficially similar they are actually very different and, given that the authors of CNM2025 only included "compounds in clinical trials as of mid-2024" in their study, I would argue that their study does not properly examine the link between Fsp³ and clinical progression. I agree that the difference between mean Fsp³ values for drugs approved up to 2009 and for drugs approved after 2009 is statistically significant. What is not clear from the analysis summarized in Fig. 1b in CNM2025 is whether the lower Fsp³ values of drugs that were approved after 2009 reflect smaller increases in Fsp³ over the course of clinical development (the B-17 has disappeared from the lunar crater) or lower Fsp³ values for compounds entering clinical development (the B-17 is still in the lunar crater). I think it's possible to address this question but you would need to analyse the data a lot more carefully than the authors of CNM2025 appear to have done. For example, you might examine the time-dependencies of mean Fsp³ values for compounds evaluated in phase 1 and the corresponding mean Fsp³ values for compounds that progressed or failed to progress to phase 2. While I consider more careful analysis of progression to be feasible I see little or no value from the perspective of real world drug discovery in actually performing the analysis more carefully.

This is a good point at which to wrap up and, unless the the trends in the data can shown to reflect causation, the debate can be described as bald men fighting over a comb (as one who is follicly challenged I always find it painful to use this phrase). I see variation in drug properties with time as an effect rather than a cause and Forrest Gump would have been well aware of this fifteen years before the publication of LBH2019 when he famously observed that "shit happens". One point on which the CNM2025 authors and I do appear to agree is that there is not currently a B-17 in a lunar crater. Where we appear to differ is that they seem to be suggesting this was because it has vanished while I never believed that it was ever there in the first place. I’ll let the late great Dave Allen have the last word.

Assembling data sets for training ML bioactivity models

Here’s a photo from one of my exercise walks in Paramin and you can see the Caribbean Sea in the distance. This is perhaps my favourite view on the walk because it means that I’ve just got to the top of a particularly brutal hill (cars sometimes struggle to get to the top and on one occasion I watched a car fail miserably in four attempts) although you can’t always see the sea as clearly as in this photo.  

The current post follows up on my post on the LR2024 study (Combining IC₅₀ or K_i Values from Different Sources Is a Source of Significant Noise). In the current post, I’ll be discussing in general terms how I might use ChEMBL to assemble data sets for training what I refer to in another post as regression-based machine learning (ML) models. These models can reasonably be described as quantitative structure-activity relationships (QSARs) because 'activity' is a continuous (as opposed to categorical) variable. However, the term 'QSAR' does appear to be less used these days, possibly reflecting the limited impact that QSAR approaches have made on real world drug discovery, and it's also much easier to persuade people that you're doing artificial intelligence (AI) if you describe your QSAR models as ML models. In this post I shall refer to regression-based ML models for biological activity simply as 'QSAR-like ML models'.

Much of the focus of AI-based drug design appears to be generation of novel chemical structures and devising synthetic routes for the associated compounds. Many who tout AI as a panacea for the ills of drug discovery appear to be assuming that predictively useful QSAR-like ML models will be available or can readily be built even in the early stages of drug discovery projects. I remain skeptical and my view is that if sufficient data are available in ChEMBL for building useful QSAR-like ML models then it is likely that somebody else has already got to where you would like to be. Nevertheless, I do see value in automating the assembly of bioactivity data sets from ChEMBL even if it does not prove feasible to build useful QSAR-like ML models and I'll also be discussing some of the ways that you might use such data sets in the early stages of a drug discovery project.

My first step when assembling a data set  (which I'll refer to as a 'bioactivity data set') for training QSAR-like ML models would be to extract from ChEMBL all (in-range) measured values for potency and affinity in assays that have been run against the target of interest. Potency and affinity should be expressed logarithmically for modelling as shown in the figure below and the relevant values are often  referred to collectively as ‘pChEMBL’ values (I note in posts here from September and December of 2024, the term is used in the literature without being defined properly). I would generally anticipate that there will be only a single pChEMBL value for most compounds and for compounds for which there are multiple pChEMBL values I would use the mean values to quantify bioactivity for these compounds. In cases where there is more than one pChEMBL value available for individual compounds I would also calculate the standard deviation when two or more pChEMBL values are available for a compounds and this can be seen as another way to assess what is referred to as assay compatibility in the LR2024 study.     

A bioactivity data set assembled in this manner would have a single bioactivity data value for each compound and I would take a look at how many compounds that data is available for because it might be possible to use this information for deciding whether or not to build a QSAR-like ML model. However, you need to be careful about using the size of the data set for making decisions like this because you can get away with with fewer data values if these are better distributed from the perspective of model-building (a view from Orwell's Animal Farm might have been: uniform good, polymodal bad) and the comment that Stalin is alleged to have made about the T-34 tank (quantity has a special quality all of its own) is perhaps not quite the ground truth that many ML modellers believe it to be. JFK's advice to ML modellers might have been: ask not whether you have enough data but whether the available data satisfy the requirements for modelling. 

My next step would be to examine the distribution of data values in the bioactivity data set. I would take a look at the spread in bioactivity values (for modelling the spread in values should be large). If the distribution of the bioactivity data set is Gaussian then a standard deviation of 0.8 log units will place 80% of the data values in a range of 2.05 log units (I used this handy Normal percentile calculator) and I wouldn't attempt to build a QSAR-like ML model if the standard deviation was less than this (unless the person 'asking' me to build the model was also going to perform my annual performance review 😁). I would also visualise the distribution of bioactivity values because a noticeably polymodal distribution should ring a few alarm bells for me (clustering in training data may cause validation procedures to arrive at optimistic assessments of model quality).

Having established an acceptable spread in the bioactivity data I would take a look at where the distribution of bioactivity values is centred. Specifically, I would not attempt to build a QSAR-like ML model unless at least 50% of the compounds in the bioactivity data set exhibited sub-micromolar activity and for a Gaussian distribution this would correspond to a mean bioactivity value of 6. If this seems a bit extreme it’s worth pointing out that to accurately measure an IC₅₀ value of 10 μM requires that the compound be soluble, while neither aggregating nor interfering with assay read-out, at a concentration of 100 μM. Problems with biochemical assays typically increase when you test compounds at higher concentrations and this is one reason that biophysical assays are generally preferred for screening fragments. With sufficient care you can run biochemical assays at high concentrations and the S2009 article by former colleagues shows how you can assess (and potentially correct for) assay interference. Inadequate aqueous solubility, however, is not something that you can generally deal with. One general difficulty when assembling bioactivity data sets from ChEMBL is that it can be very difficult to assess how carefully low affinity compounds have been assayed.

Before starting to assemble a data set for training QSAR-like ML models I would also assess the target from an assay perspective (in a real world drug discovery scenario this assessment would be done in collaboration with bioscientists). In particular, I would be looking for indications, such as k_inact values being reported, of activity being due to irreversible mechanisms of action. The bioactivity of an irreversible covalent inhibitor can be considered to be 'two-dimensional' (affinity for formation of non-covalently bound target-ligand complex and rate constant for covalent bond formation) and I'll point you to S2016 and McW2021 for more information.  It is important to have sufficient spread both in the k_inact and in K_i values when building QSAR-like ML models for irreversible inhibitors and you also need to be aware of any limits that the assays place on values that can reliably quantified. It is common for IC₅₀ values to be reported in the literature for irreversible inhibitors although you can use such data in drug discovery if you run the assays carefully (see T2021). However, it's important to bear in mind that using a single data value to quantify the bioactivity of an irreversible inhibitor necessarily results in information loss and that the ChEMBL curation procedures do not generally capture assay protocols at the level of detail that would be required for combining IC₅₀ values from different studies even when inhibition is reversible. This should not be taken as a criticism of ChEMBL and I consider recording assay protocols in this level of detail to be well beyond the call of duty for those curating the bioactivity data.   

Now let’s take a look at scenario in which the objective is to initiate a drug discovery project (as opposed to merely building QSAR-like ML models for the purpose of publication). One point that I really do need to stress is that you’re far from helpless if the data available in ChEMBL do not satisfy the requirements for building QSAR-like ML models. First, you can try to source structural analogs of bioactive compounds (there are many more options these days for doing this than when I worked in industry and you can also look beyond ChEMBL, in patents for example, when identifying bioactive compounds) and, in any case, you’re going to need to source pure samples for compounds to check that they are indeed bioactive. Second, you can use the use structures of the active compounds to set up queries for pharmacophore matching and molecular shape matching (see GGP1996 | N2010). Third, if structural information is available for the target you can investigate how the active compounds might be interacting with the target and use this information to source potentially active compounds (these days it is feasible to use free energy calculations to predict affinity in addition to the scoring functions that have long been used for virtual screening and I’ll point you to C2021 | MH2023 | C2023). Fourth, you can look for structure-activity relationships (see SHC2005 for an early example of this and the more recent S2025 study which provides software) in the bioactivity data and one way of achieving this is to search for ‘activity cliffs' (significant differences in bioactivity for pairs of structurally similar compounds; see M2006 | GvD2008 | SB2012 | SHB2019 | vT2022  ) or more generally by analysing bioactivity of neighbourhoods around bioactive compounds. Fifth, you can look for instances of increased polarity, such as replacement of aromatic CH with aromatic N) being well-tolerated from the perspective of bioactivity (this can be thought of both in terms of lipophilic efficiency and as a variation on the activity cliff theme). I should point out that the approaches that I've mentioned in this paragraph can be accommodated within an AI framework if you're prepared to think beyond ML in your definition of AI.

Let’s now suppose that you can satisfy the data requirements or building QSAR-like ML models for the target of interest with data in ChEMBL. Does this mean that you can whip up some QSAR-like ML models, fire up your generative AI and have clinical candidates condensing out of the ether? I think not and one implication of being able to satisfy the data requirements for building QSAR-like ML models is that others will have worked hard in the past trying to get to where you’d like to be in the future. Before you even start to build QSAR-like ML models you’ll need to assess the earlier work from the perspectives of both intellectual property and understanding why it didn't lead to clinical candidates. There are many rabbit holes that you can disappear down in drug discovery and here’s some advice from Otto von Bismarck (ironically it was a young, emotionally unstable, half-English Kaiser with a withered arm who brought down the Iron Chancellor): 

Only a fool learns from his own mistakes. The wise man learns from the mistakes of others.

If the available data do indeed satisfy the requirements for building QSAR-like ML models then it’s a pretty safe assumption that many of the data values will correspond to compounds from one or more structural series (see Figure 1 below which was taken from a previous post). Under this scenario the distribution of data points in the descriptor space is likely to be very uneven and you should anticipate that ‘global’ QSAR-like ML models built using such data will actually be ensembles of local models. One consequence of what I sometimes refer to as ‘clustering’ in the descriptor space is that what you might think is an interpolation is actually an extrapolation (take a look at the point highlighted by the arrow in Figure 1). Clustering in the descriptor space can also cause validation procedures to arrive at optimistic assessments of model quality because most data points have close neighbours and this can lead to overfitting (I discovered at EuroQSAR back in 2016 that some consider it rather uncouth to mention the H2003 study). Correlations between descriptors and related metrics such as Mahalanobis distance become less meaningful when there is a lot of clustering in the descriptor space. This in turn has implications for principal component analysis (commonly used to assess dimensionality of data sets and eliminate correlations between descriptors) and for methods such as PLS (see K1999) that aim to account for correlations between descriptors in regression analysis.

 

For reasons outlined in the previous paragraph I wouldn’t generally combine data from different structural series when building QSAR-like ML models. I would, however, look for relationships between different structural series by, for example, aligning their defining scaffolds (or structural prototypes if you prefer) because this may allow the SAR observed for one scaffold to be overlaid onto another scaffold. Before attempting to build a QSAR-like ML model I would plot pIC₅₀ of against calculated logP for structural series of interest with a view to assessing response of bioactivity to increased lipophilicity (a weak correlation between bioactivity and lipophilicity is desirable but if this is not the case then the response should be at least be relatively steep). I would also fit a straight line to the plot of pIC₅₀ versus calculated logP because this allows the steepness of the response to be quantified and the residuals can be used (as discussed in ‘Alternatives to ligand efficiency for normalization of affinity’ section of K2019) to quantify the extent to which individual pIC₅₀ values beat the trend in the data (this information can be useful to medicinal chemists who wish think about SAR although I have to admit that "the most interesting SAR is likely to be associated with the most deviant values" actually refers youthful antics of the Honourable former Member for Witney). Having performed these simple analyses of the bioactivity data I would attempt to build QSAR-like ML models for each structural series of interest.  

This is a good point at which to wrap up and I'll share some thoughts on the use of QSAR-like ML models in drug design. Back in 2009 I discussed (see K2009) the difference between hypothesis-driven molecular design and prediction-driven molecular design and I suggest that the former can be accommodated within an AI design framework. Some who assert the value of QSAR-like ML models for drug design appear to treat drug design as an exercise in prediction and I've been crapping on for quite a few years (see this post from January 2015) is that it is more appropriately seen in a Design of Experiments framework (generate the necessary data as efficiently as possible). For many drug discovery projects the available data will not satisfy the requirements for building QSAR-like ML models until relatively late in the project and in some cases clinical candidates will be discovered without ever being able to satisfy the data requirements for building QSAR-like ML models (this is more likely to be the case when bioactivity cannot be represented by a single data value as is the case for modalities such as irreversible inhibition and targeted protein degradation). I consider it essential to account for numbers of adjustable parameters and for correlations between descriptors (or features if you prefer) when building QSAR-like ML models, and I’m also concerned that the challenges presented by clustering in descriptor spaces are not properly acknowledged. It also needs to be said that it is consideration of exposure that differentiates drug design from ligand design and I recommend that everybody working in drug discovery and chemical biology read the SR2019 article. 

 

Property Forecast Index Validated

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I arrived in Korea on Friday night and am greatly enjoying it here. Photos below show the Jungbu Dried Seafoods Market near where I'm staying and dinner on Sunday (spicy beef noodles).

I visited the War Memorial on Sunday and took selfies with the Shenyang J-6 (Chinese version of MiG-19) 'liberated' by Capt. Lee Woong-pyeong when he defected to South Korea on 25th February 1983, a 'liberated' T-34 (as Uncle Joe is said to have observed, quantity has a quality all of its own) and Great Leader's car (also 'liberated' although it was not clear exactly when). 

So enough of the travel photos for now and let's get back to the science. Regular readers (both of them) of this blog will be well aware of my visceral dislike for drug design metrics. One reason for this visceral dislike is that I consider these metrics to trivialise the problems faced by medicinal chemists and I remain sceptical that one can make meaningful predictions of developability or likelihood of clinical success for compounds based only on their chemical structures without knowing anything about their biological activities. One metric that I have criticised harshly in the past is property forecast index (PFI) which was originally introduced as solubility forecast index (SFI). Specifically, I denounced SFI as a ‘draw pictures and wave arms’ data analysis strategy and privately I even considered the possibility that it had been created by a toddler armed with a box of colored crayons.

Let’s take a look at the HY2010 article in which SFI was introduced. Proprietary aqueous solubility measurements (continuous variable) were first processed to assign compounds to one of three aqueous solubility categories. Histograms showing the proportions of measurements in each aqueous solubility category were created by binning values of SFI and of c log D_pH7.4 and the histograms were compared visually:    

This graded bar graph (Figure 9) can be compared with that shown in Figure 6b to show an increase in resolution when considering binned SFI versus binned c log D_pH7.4 alone.

Recently, I have been forced to revise my negative view of PFI and I have to admit that it pains me deeply to realise that I could have been so utterly wrong for so long in my assessment of what is actually an elegant and highly-predictive drug design metric. Indeed I have now come to the conclusion that the only reason that the Journal of Medicinal Chemistry did not include PFI in its nomination for the Nobel Prize in Physiology or Medicine was that the introduction of the Ro5, LipE and Fsp3 principles led directly to so many marketed drugs being approved.

What has caused such a fundamental shift in my views? First, PFI is highlighted in the European Federation of Medicinal Chemistry (EFMC) ‘Best Practices from Hits to Lead Generation’ webinar.  Now it goes without saying that EFMC includes some of the sharpest minds in medicinal chemistry and, given that they consider PFI to be sufficiently important for inclusion in a best practices webinar, it became abundantly clear that I needed to revise my hopelessly naïve thinking. Let’s join the webinar at 27:53 and you’ll see in the webinar slide that SFI (as PFI was originally introduced) has been strongly endorsed by Practical Cheminformatics, a blog that many, including me, accept without question as the source of a number of fundamental ground truths in the AI field.

However, what convinced me of the sublime elegance and extreme predictivity of PFI is a seminal study by the world-renowned expert on tetrodotoxin pharmacology, Prof. Angelique Bouchard-Duvalier of the Port-au-Prince Institute of Biogerontology, working in collaboration with the Budapest Enthalpomics Group (BEG). The manuscript has not yet been made publicly available although I was able to access it with the help of my associate ‘Anastasia Nikolaeva’ (not sure exactly what she’s doing these days although she did post a photo from Pyongyang showing her and a burly chap with a toothy grin and a bizarre haircut). There is no doubt that this genuinely disruptive study will comprehensively reshape the predictive ADME landscape, enabling drug discovery scientists, for the very first time, to make accurate predictions for developability and probability of critical trial success using only chemical structures as input.

Prof. Bouchard-Duvalier’s seminal study clearly demonstrates that graphical presentation of categorized continuous data outperforms regression analysis performed on the uncategorized continuous data. The math is truly formidable (my rudimentary understanding of Haitian patois didn’t help either) and involves first projecting the atomic isothermal compressibility matrix into the quadrupole-normalized polarizability tensor before applying the Barone-Samedi transformation, followed by hepatic eigenvalue extraction using an algorithm devised by E. V. Tooms (a reclusive Baltimore resident whose illustrious research career in analytic topology was abruptly halted almost 31 years ago by an unfortunate escalator accident). The incisive analysis of Prof. Bouchard-Duvalier shows without a shadow of doubt that the data visualization used to establish PFI as a fundamental drug design principle will reliably and robustly outperform all AI approaches to prediction of aqueous solubility. Furthermore, ‘Anastasia Nikolaeva’ was also able to ‘liberate’ a prepared press release in which the beaming BEG director Prof. Kígyó Olaj explains that, “Possibilities are limitless now that we can accurately and robustly predict the developability of a compound using only its chemical structure as input and we can now finally consign regression analysis to the dustbin of history. Surely the Editors of Journal of Medicinal Chemistry will recognize the impact of PFI on real world drug discovery when they make their Nobel Prize nominations later this year.” 

Thinking About Aqueous Solvation

Given that it was International Women's Day yesterday, I'll open the the post (and blogging for 2025) with a photo of a gravestone at St James' Church in Bramley (Hampshire).

In the current post I’ll be taking a look at some aspects of aqueous solvation and Richard Wolfenden’s 1983 “Waterlogged Molecules” article (W1983) is still worth reading today (as an aside, Prof Wolfenden will turn ninety in May of this year and hopefully mentioning this won't put what is called "goat mouth" in my native Trinidad and Tobago on him as I did for Oscar Niemeyer with the words "ele vive ainda" while studying Portuguese in 2012). As noted in W1983 the formation of a target-ligand complex requires partial desolvation of both target and ligand:

When biological compounds combine, react with each other, or change shape in watery surroundings, solvent molecules tend to be reorganized in the neighborhood of the interacting groups.

Formation of a target-ligand can also be seen as an “exchange reaction” and this point is very well made in SGT2012:

Molecular binding in an aqueous solvent can be usefully viewed not as an association reaction, in which only new intermolecular interactions are introduced between receptor and ligand, but rather as an exchange reaction in which some receptor–solvent and ligand–solvent interactions present in the unbound state are lost to accommodate the gain of receptor–ligand interactions in the bound complex.

In HBD3 I briefly discuss ‘frustrated hydration’ as a phenomenon that could be exploited in drug design and I’ll quote from the Summary section of W1983:  

When two or more functional groups are present within the same solute molecule, their combined effects on its free energy of solvation are commonly additive. Striking departures from additivity, observed in certain cases, indicate the existence of special interactions between different parts of a solute molecule and the water that surrounds it.

I’ll try to explain how this could work for ligand design and let’s suppose that we have two polar atoms that are close together in the binding site. The proximity of the polar atoms in the binding site means that water molecules forming ideal interactions with the polar atoms in the binding sites are also likely to be close together. However, the mutual proximity of the water molecules can lead to unfavourable interactions between the water molecules which ‘frustrate’ the (simultaneous) hydration of the two polar atoms in the binding site. Now if we design a ligand with two polar atoms positioned to form good interactions with polar atoms in the binding site it is likely that these will also be in close proximity and that their hydration will be similarly frustrated. I would generally anticipate that frustration of hydration will not be handled well by implicit solvent models (RT1999 | FB2004 | CBK2008 |  KF2014)  or computational tools such as WaterMap that calculate energetics for individual water molecules (especially in cases where the two hydration sites cannot be simultaneously occupied).

To illustrate frustration of hydration I’ve taken a graphic from a talk from 2023. The unfavorable interactions between solvating water molecules that frustrate hydration are shown as red double-headed water molecules (in some cases these interactions will be repulsive to the extent that only one of the hydration sites can be occupied at a time). You’ll also notice two thick green lines in the right hand panel and these show secondary interactions that stabilize the bound complex. Secondary interactions of this nature were discussed in a molecular recognition context in the JP1990 study and the observation (see A1989) that pyridazine is a better hydrogen bond acceptor (HBA) than its pK_a would have you believe can be seen in a similar light.  Secondary interactions like these only enhance affinity when the proximal polar atoms are of the same ‘type’ (the proximal polar atoms in the 1,8-naphthyridine are both HBAs) and we should anticipate that the secondary interactions for the contact between pyrazole and the ‘hinge’ of a tyrosine kinase will be deleterious for affinity. In contrast to secondary interactions, frustration of hydration can be beneficial for affinity even when the proximal polar atoms are of opposite types, as would be the case for an HBA that is near to a hydrogen bond donor (HBD).     

While it is clearly important to account for aqueous solvation when using physics-based approaches for prediction of binding affinity, passive permeability and aqueous solubility, the measurement of gas-to-water transfer free energy is not exactly routine (I’m not aware that any companies offer measurement aqueous solvation energy as a service nor do I believe that this is an activity that would readily funded). Measurements for aqueous solvation energy reported in the literature tend to be for relatively volatile compounds and I’ll direct readers to the C1981, W1981 and A1990 studies.

A view is that I've held for many years is that a partition coefficient could be used as an alternative to gas-to-water transfer free energy for studying aqueous solvation. It's also worth noting that when we think about desolvation in drug design we're often considering the energetic cost of bringing polar atoms into contact with non-polar atoms (as opposed to transferring the polar atoms to gas phase). Partition coefficient measurement is a lot more routine than solvation free energy measurement and most drug discovery scientists are of aware that the octanol/water partition coefficient (usually quoted as its base 10 logarithm logP) is an important design parameter. However, the octanol/water partition coefficient is not useful for assessing aqueous solvation because the hydroxyl group of octanol can form hydrogen bonds with solutes and the water-saturated solvent is actually quite 'wet' (the DC1992 study reports that the room temperature solubility of water in octanol is 2.5 M). If we’re going to use partition coefficient measurements for studying aqueous solvation then I would argue that we should make these measurements with a saturated hydrocarbon such as cyclohexane or hexadecane that lacks hydrogen bonding capability.

Here’s another slide from that 2023 talk showing that pyridine is lipophilic for octanol/water but hydrophilic for hexadecane/water. The difference in the logP values for a solute is sometimes referred to as ΔlogP (it is equivalent to the hexadecane/water logP value with both solvents water-saturated) and can be considered to quantify the solute’s ability to form hydrogen bonds (see Y1988 | A1994 | T2008). I'll mention in passing that ΔlogP measurements with toluene as the less polar organic solvent have been used to study intramolecular hydrogen bonding (see S2013 | C2016 | C2018).     

It should be stressed  that people have been thinking about using different organic solvents for partition coefficient measurement for a lot longer than me. My view, expressed in K2013, is that the justification in H1963 for using octanol was partly based on a misinterpretation of Collander's C1951 study. I really like this quote from Alan Finkelstein's 1976 article (as an aside the partition coefficient literature is not exactly awash with alkane/water logP measurements for amides and the article reports measured values of the hexadecane/water partition coefficient for acetamide, formamide, urea, butyramide and isobutyramide): 

It has long been fashionable to worry about which organic solvent (and polarity) is the best model for the lipoidal region of a particular cell membrane (Collander, 1954). These solvents have ranged from isobutanol (the most polar) to olive oil (the least polar). I have never understood the point of this. If the lipoidal region of the plasma membrane is a lipid bilayer, then clearly the appropriate model solvent is hydrocarbon. For artificial bilayers this is obviously so. I chose n-hexadecane as the particular hydrocarbon, because its chain length is comparable to that of the fatty acid residues in most phospholipids, and it is conveniently available.

I also need to mention the B2016 study (Blind prediction of cyclohexane–water distribution coefficients from the SAMPL5 challenge) since the the cyclohexane/water distribution coefficient was used as a surrogate for gas-to-water transfer free energy in the challenge:

The inclusion of distribution coefficients replaces the previous focus on hydration free energies which was a fixture of the past five challenges (SAMPL0-4) [1 | 2 | 3 | 4 | 5 | 6 | 7]. Due to a lack of ongoing experimental work to generate new data, hydration free energies are no longer a practical property to include in blind challenges. It has become increasingly difficult to find unpublished or obscure hydration free energies and therefore impossible to design a challenge focusing on target compounds, functional groups or chemical classes.

I consider initiatives such as the SAMPL5 cyclohexane/water distribution challenge to be valuable for assessing model predictivity in an objective and transparent manner. Generally, I would avoid including logD measurements for compounds that are significantly ionized under experimental conditions because these require that account be taken of ionization when making predictions (better to measure logD at a pH at which ionizable functional groups are not significantly ionized). While challenges such as SAMPL5 are certainly valuable for assessment of predictivity of models, I consider them less useful in model development which requires measured data for structurally-related compounds. 

The isosteric pairs 1/2  and 3/4 shown in the graphic below will give you an idea of what I'm getting at. The predicted pK_BHX values taken from K2016 suggest that 1 is less polar than than its isostere 2 and I'd expect 3 to be more polar than 4.

While the three N-butylated purines shown in the graphic below are not strictly isosteric I would consider it valid to interpret the cyclohexane/water logP values taken from S1998 as reflecting differences in hydrogen bond acceptor strength.

This is a good point at which wrap up and, given the fundamental importance of aqueous solvation in biomolecular recognition and drug design, I see tangible advantages in having a large body of measured data in the public domain. My view is that to measure gas-to-water transfer free energy for significant numbers of compounds of interest to drug discovery scientists would be both technically demanding and unlikely to get funded although I would be delighted to be proven wrong on either point. This means that we need to learn to use other types of data in order to study aqueous solvation and my view is that an alkane/water partition coefficient would be the best option. Using alkane/water partition coefficients as an alternative to gas-to-water transfer free energies for studying aqueous solvation would also enable enthalpic (see RT1984) and volumetric aspects of aqueous solvation to be investigated more easily.